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Because mod(x) is not "smooth at x = 0.
Suppose f(x) = mod(x). Then f'(x), if it existed, would be the limit, as dx tends to 0, of [f(x+dx) - f(x)]/dx
= limit, as dx tends to o , of [mod(x+dx) - mod(x)]/dx
When x = 0, this simplifies to mod(dx)/dx
If dx > 0 then f'(x) = -1
and
if dx < 0 then f'(x) = +1
Consequently f'(0) does not exist and hence the derivative of mod(x) does not exist at x = 0.
Graphically, it is because at x = 0 the graph is not smooth but has an angle.
Because mod(x) is not "smooth at x = 0.
Suppose f(x) = mod(x). Then f'(x), if it existed, would be the limit, as dx tends to 0, of [f(x+dx) - f(x)]/dx
= limit, as dx tends to o , of [mod(x+dx) - mod(x)]/dx
When x = 0, this simplifies to mod(dx)/dx
If dx > 0 then f'(x) = -1
and
if dx < 0 then f'(x) = +1
Consequently f'(0) does not exist and hence the derivative of mod(x) does not exist at x = 0.
Graphically, it is because at x = 0 the graph is not smooth but has an angle.
Because mod(x) is not "smooth at x = 0.
Suppose f(x) = mod(x). Then f'(x), if it existed, would be the limit, as dx tends to 0, of [f(x+dx) - f(x)]/dx
= limit, as dx tends to o , of [mod(x+dx) - mod(x)]/dx
When x = 0, this simplifies to mod(dx)/dx
If dx > 0 then f'(x) = -1
and
if dx < 0 then f'(x) = +1
Consequently f'(0) does not exist and hence the derivative of mod(x) does not exist at x = 0.
Graphically, it is because at x = 0 the graph is not smooth but has an angle.
Because mod(x) is not "smooth at x = 0.
Suppose f(x) = mod(x). Then f'(x), if it existed, would be the limit, as dx tends to 0, of [f(x+dx) - f(x)]/dx
= limit, as dx tends to o , of [mod(x+dx) - mod(x)]/dx
When x = 0, this simplifies to mod(dx)/dx
If dx > 0 then f'(x) = -1
and
if dx < 0 then f'(x) = +1
Consequently f'(0) does not exist and hence the derivative of mod(x) does not exist at x = 0.
Graphically, it is because at x = 0 the graph is not smooth but has an angle.
Because mod(x) is not "smooth at x = 0.
Suppose f(x) = mod(x). Then f'(x), if it existed, would be the limit, as dx tends to 0, of [f(x+dx) - f(x)]/dx
= limit, as dx tends to o , of [mod(x+dx) - mod(x)]/dx
When x = 0, this simplifies to mod(dx)/dx
If dx > 0 then f'(x) = -1
and
if dx < 0 then f'(x) = +1
Consequently f'(0) does not exist and hence the derivative of mod(x) does not exist at x = 0.
Graphically, it is because at x = 0 the graph is not smooth but has an angle.
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What is the derivative of mod x?
x/mo x
What is the derivative of 2lnx?
The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x
What is the derivative of 3cosx?
The derivative of 3cos(x) is -3sin(x). This can be found using the chain rule, which states that the derivative of a composition of functions is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. In this case, the derivative of cos(x) is -sin(x), and when multiplied by the constant 3, we get -3sin(x) as the derivative of 3cos(x).
What is the derivative of csc x?
The derivative of csc(x) is -cot(x)csc(x).
What is the derivative of sec squared x?
derivative of sec2(x)=2tan(x)sec2(x)
What is the derivative of mod x?
x/mo x
What is the first derivative of a mod b?
The derivative of f(x) = x mod b is f'(x)=1, except where x is a multiple of b, when it is undefined.
When does the derivative of a function exist at a given point?
Let f be a function and a be the given point you are considering. Then,f(x) - f(a)---------------(x-a)is the difference quotient. If the limit as x approaches a exists, then the function is differentiable at a, or we say the derivative exists at a. If that limit does not exist, then the derivative does not exist at that point.
Why absolute value of x is not differentiable at point 0?
The absolute value of x, |x|, is defined as |x| = x, x>=0; -x, x<0. If you derive this, then you will find that the derivative is 1 when x>=0, and -1 when x<0. But this means that the derivative as x approaches 0 from the left does not equal the derivative as x approaches 0 from the right, as -1=/=1. So the limit as x approaches 0 does not exist, and therefore the gradient does not exist at that point, and so |x| cannot be differentiated at x = 0.
What is the derivative of 2lnx?
The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x
Derivative of cosx?
The derivative of cos(x) is negative sin(x). Also, the derivative of sin(x) is cos(x).
What is the derivative of 3cosx?
The derivative of 3cos(x) is -3sin(x). This can be found using the chain rule, which states that the derivative of a composition of functions is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. In this case, the derivative of cos(x) is -sin(x), and when multiplied by the constant 3, we get -3sin(x) as the derivative of 3cos(x).
What is the derivative of sinΟx?
The derivative with respect to 'x' of sin(pi x) ispi cos(pi x)
What is the derivative of csc x?
The derivative of csc(x) is -cot(x)csc(x).
What is the derivative of secant x?
The derivative of sec(x) is sec(x) tan(x).
What is the derivative of cotx?
The derivative of cot(x) is -csc2(x).
What is the second derivitive of sec x?
Write sec x as a function of sines and cosines (in this case, sec x = 1 / cos x). Then use the division formula to take the first derivative. Take the derivative of the first derivative to get the second derivative. Reminder: the derivative of sin x is cos x; the derivative of cos x is - sin x.
